To begin, use the `mongoexport` utility to export the data from MongoDB. This tool is included with MongoDB distributions and allows you to export data in JSON or CSV format. Execute the following command to export your data as JSON:
```bash
mongoexport --db yourDatabase --collection yourCollection --out data.json
```
Replace `yourDatabase` and `yourCollection` with your actual database and collection names. This will create a `data.json` file that contains your MongoDB data.

Upload the exported JSON file (`data.json`) to your Databricks File System (DBFS). You can do this by using the Databricks UI to drag and drop the file or by using the Databricks CLI or REST API to programmatically upload the file.

Open your Databricks workspace and create a new notebook. This notebook will contain the code needed to read, process, and store your data in the Databricks Lakehouse.

Use the following PySpark code in your Databricks notebook to read the JSON data from DBFS into a DataFrame:
```python
from pyspark.sql import SparkSession
spark = SparkSession.builder.getOrCreate()
df = spark.read.json('/dbfs/path/to/data.json')
```
Replace `/dbfs/path/to/data.json` with the actual path of your JSON file in DBFS.

If your data requires any transformation, such as data cleaning or restructuring, perform these operations using Spark DataFrame operations. For example, you could filter out unnecessary columns or handle missing values:
```python
df = df.select('column1', 'column2').filter(df['column3'] > 0)
```

Once your data is ready, write it to Delta Lake, which is the storage format that powers Databricks Lakehouse. You can write the data as follows:
```python
df.write.format('delta').mode('overwrite').save('/mnt/delta/your-delta-table')
```
Adjust the path `/mnt/delta/your-delta-table` to your desired location in the Databricks Lakehouse.

Finally, verify that your data has been successfully transferred and stored in the Databricks Lakehouse by reading back the data and performing some basic checks:
```python
df_delta = spark.read.format('delta').load('/mnt/delta/your-delta-table')
df_delta.show()
```
This step ensures that the data is accessible and correctly stored in the desired format.
By following these steps, you can effectively move data from MongoDB to Databricks Lakehouse without relying on third-party connectors or integrations.